Chapter 6

Interest Rates and Bond Valuation

Bond Definitions

• Bond

• Par value (face value)

• Coupon rate

• Coupon payment

• Maturity date

• Yield or Yield to maturity

PV of Cash Flows as Rates Change

• Bond Value = PV of coupons + PV of par (also known as face value)

• Bond Value = PV annuity + PV of lump sum

• Remember, as interest rates increase the PVs decrease

• So, as interest rates increase, bond prices decrease and vice versa

Bond Prices: Relationship Between Coupon and Yield

• If YTM = coupon rate, then par value = bond price. To be sure, let’s verify with an example.

• If YTM > coupon rate, then par value > bond price– Why?– Selling at a discount, called a discount bond

• If YTM < coupon rate, then par value < bond price– Why?– Selling at a premium, called a premium bond

The Bond-Pricing Equation

tr)(1

F

r

tr)(1

1-1

C ValueBond

Interest Rate Risk

• Change in price due to changes in interest rates– Interest rates up, bond price down!– Long-term bonds have more interest rate risk

than short-term bonds• More-distant cash flows are more adversely

affected by an increase in interest rates– Lower coupon rate bonds have more interest rate

risk than higher coupon rate bonds• More of the bond’s value is deferred to maturity

(thus, for a longer time) if the coupons are small

Computing YTM

• Yield-to-maturity is the rate implied by the current bond price

• Finding the YTM requires trial and error if you do not have a financial calculator and is similar to the process for finding r with an annuity

• If you have a financial calculator, enter N, PV, PMT and FV, remembering the sign convention (PMT and FV need to have the same sign; PV the opposite sign)

Differences Between Debt and Equity

• Debt– Not an ownership interest– Creditors do not have voting

rights– Interest is considered a cost of

doing business and is tax-deductible

– Creditors have legal recourse if interest or principal payments are missed

– Excess debt can lead to financial distress and bankruptcy

• Equity– Ownership interest– Common stockholders vote to

elect the board of directors and on other issues

– Dividends are not considered a cost of doing business and are not tax deductible

– Dividends are not a liability of the firm until declared. Stockholders have no legal recourse if dividends are not declared

– An all-equity firm cannot go bankrupt

The Bond Indenture

• Contract between the company and the bondholders and includes– The basic terms of the bonds– The total amount of bonds issued– A description of property used as security, if

applicable– Sinking fund provisions– Call provisions– Details of protective covenants

Bond Classifications

• Registered vs. Bearer Forms• Security

– Collateral – secured by financial securities– Mortgage – secured by real property, normally

land or buildings– Debentures – unsecured– Notes – unsecured debt with original maturity

less than 10 years

• Seniority

Bond Characteristics andRequired Returns

• The coupon rate is usually set close to the yield, which depends on the risk characteristics of the bond when issued

• Which bonds will have the higher coupon, all else equal?– Secured debt versus a debenture

– Subordinated debenture versus senior debt

– A bond with a sinking fund versus one without

– A callable bond versus a non-callable bond

Bond Ratings – Investment Quality

• High Grade– Moody’s Aaa and S&P AAA – capacity to pay is

extremely strong– Moody’s Aa and S&P AA – capacity to pay is very

strong

• Medium Grade– Moody’s A and S&P A – capacity to pay is strong, but

more susceptible to changes in circumstances– Moody’s Baa and S&P BBB – capacity to pay is

adequate, adverse conditions will have more impact on the firm’s ability to pay

Bond Ratings - Speculative

• Low Grade– Moody’s Ba, B, Caa and Ca– S&P BB, B, CCC, CC– Considered speculative with respect to capacity

to pay. The “B” ratings are the lowest degree of speculation.

• Very Low Grade– Moody’s C and S&P C – income bonds with no

interest being paid– Moody’s D and S&P D – in default with principal

and interest in arrears

Government Bonds

• Treasury Securities– Federal government debt– T-bills – pure discount bonds with original maturity of one year or

less– T-notes – coupon debt with original maturity between one and

ten years– T-bonds coupon debt with original maturity greater than ten

years• Municipal Securities

– Debt of state and local governments– Varying degrees of default risk, rated similar to corporate debt– Interest received is tax-exempt at the federal level

Zero Coupon Bonds

• Make no periodic interest payments (coupon rate = 0%)

• The entire yield-to-maturity comes from the difference between the purchase price and the par value

• Cannot sell for more than par value• Sometimes called zeroes, or deep discount

bonds• Treasury Bills and principal-only Treasury strips

are good examples of zeroes

Floating Rate Bonds

• Coupon rate floats depending on some index value

• Examples – adjustable rate mortgages and inflation-linked Treasuries

• There is less price risk with floating rate bonds– The coupon floats, so it is less likely to differ

substantially from the yield-to-maturity• Coupons may have a “collar” – the rate cannot

go above a specified “ceiling” or below a specified “floor”

Other Bond Types

• Disaster bonds• Income bonds• Convertible bonds• Put bond• There are many other types of provisions that

can be added to a bond and many bonds have several provisions – it is important to recognize how these provisions affect required returns

Bond Markets

• Primarily over-the-counter transactions with dealers connected electronically

• Extremely large number of bond issues, but generally low daily volume in single issues

• Makes getting up-to-date prices difficult, particularly on small company or municipal issues

• Treasury securities are an exception

Inflation and Interest Rates

• Real rate of interest – change in purchasing power

• Nominal rate of interest - quoted rate of interest Reflects change in purchasing power and inflation

• The ex ante nominal rate of interest includes our desired real rate of return plus an adjustment for expected inflation

The Fisher Effect

• The Fisher Effect defines the relationship between real rates, nominal rates and inflation

• (1 + R) = (1 + r)(1 + h), where– R = nominal rate– r = real rate– h = expected inflation rate

• Approximation– R = r + h

Term Structure of Interest Rates

• Term structure is the relationship between time to maturity and yields, all else equal

• It is important to recognize that we pull out the effect of default risk, different coupons, etc.

• Yield curve – graphical representation of the term structure– Normal – upward-sloping, long-term yields are

higher than short-term yields– Inverted – downward-sloping, long-term yields

are lower than short-term yields

Figure 6.6 – Upward-Sloping Yield Curve

Factors Affecting Required Return

• Default risk premium – remember bond ratings• Taxability premium – remember municipal

versus taxable• Liquidity premium – bonds that have more

frequent trading will generally have lower required returns

• Anything else that affects the risk of the cash flows to the bondholders, will affect the required returns

Pure Expectations Theory

• Pure Expectations Theory says that an investor will get the same return regardless if she invests in a one-year security and rolls over the proceeds into another one-year security, or invests in a two-year security.

t=0 1 2

$*(1+i1) (1+?) = (1+i2)2